A national difference in differences analysis of the effect of PM_2.5 on annual death rates

Abstract

Many studies have reported that PM_2.5 was associated with mortality, but these were criticized for unmeasured confounding, not using causal modeling, and not focusing on changes in exposure and mortality rates. Recent studies have used propensity scores, a causal modeling approach that requires the assumption of no unmeasured confounders.

We used differences in differences, a causal modeling approach that focuses on exposure changes, and controls for unmeasured confounders by design to analyze PM_2.5 and mortality in the U.S. Medicare population, with 623, 036, 820 person-years of follow-up, and 29, 481, 444 deaths. We expanded the approach by clustering ZIP codes into 32 groups based on racial, behavioral and socioeconomic characteristics, and analyzing each cluster separately. We controlled for multiple time varying confounders within each cluster. A separate analysis examined participants whose exposure was always below 12 μg/m³. We found an increase of 1 μg/m³ in PM_2.5 produced an increased risk of dying in that year of 3.85 × 10⁻⁴ (95% CI 1.95 × 10⁻⁴, 5.76 × 10⁻⁴). This corresponds to 14,000 early deaths per year per 1 μg/m³. When restricted to exposures below 12 μg/m³, the increased mortality risk was 4.26 × 10⁻⁴ (95% CI 1.43 × 10⁻⁴, 7.09 × 10⁻⁴). Using a causal modeling approach robust to omitted confounders, we found associations of PM_2.5 with increased death rates, including below U.S. and E.U. standards.

1. Introduction

The Clean Air Act requires the US Environmental Protection Agency (EPA) to set National. Ambient Air Quality Standards (NAAQS) to protect vulnerable populations with an adequate margin of safety. Many studies have reported associations of PM_2.5 and mortality and morbidity following long and short-term exposure (Abu Awad et al., 2019; Beelen et al., 2014; Crouse et al., 2015; Di et al., 2017; Hoek et al., 2013; Pinault et al., 2016; Pope et al., 2019; Vodonos, 2018). These were undertaken by many investigators with over 50 cohorts in the most recent PM_2.5 meta-analysis (Vodonos, 2018), and have resulted in EPA sequentially tightening the PM_2.5 standard. The global burden of disease ranks air pollution among the largest public health risks.

Recent studies have reported associations between PM_2.5 and mortality at concentrations below the 2012 U.S. EPA NAAQS or World Health Organization air quality guidelines (Di et al., 2017; Wang et al., 2016; Yang et al., 2012). However, some have criticized many of these studies for not using causal modeling approaches.

Causal modeling methods can aid in assessing causality. The general approach is to try to make an observational study closely mimic a randomized trial. In addition, causal methods provide marginal estimates of the effects of exposure, that do not depend on the distribution of the covariates in the study population (Imai and van Dyke, 2004). A common approach is to use propensity score matching or inverse probability weighting to make the exposure independent of all measured confounders (Baccini et al., 2017; Rubin, 1997). Recent studies have used that approach to examine the association of PM_2.5 with mortality, and provided robust findings (Abu Awad et al., 2019; Schwartz et al., 2018; Wei et al., 2020; Wu, 2020; Yitshak-Sade, 2019). However, propensity scores only control for measured confounders, and therefore do not address the argument that there is unmeasured confounding. Hence it is important to complement that approach using methods that can address unmeasured confounders.

Approaches that control for unmeasured confounders by design include difference-in-differences (DID) analyses (Wang et al., 2016; Yitshak-Sade, 2019). In a classical DID model, the mean response is calculated for the exposed and non-exposed groups in pre-exposure and post-exposure periods. Since all slowly varying predictors of outcome such as socioeconomic status (SES), smoking, obesity, etc. are the same in each group in both periods, the difference between outcomes in the two periods in the exposed group cannot be confounded by those variables. The difference between pre-exposure and post-exposure periods in the unexposed group is a negative outcome control for the difference in the exposed group. It controls for changes in an outcome due to covariates that can change between periods similarly between the two locations. The difference in these pairs of differences is a causal estimate, assuming that no other exposure has affected the two groups differently over time (Donald and Lang, 2007). Because the DID approach examines the effect of changes in exposure (post vs pre periods) on change in outcome, it is precisely the type of study that EPA’s CASAC says it prefers. The method has been generalized to look at more than two locations, more than two time periods, and continuous, time varying exposures (Wang et al., 2016). With multiple locations time-invariant omitted confounders are controlled using an indicator variable for each location. However, it still require the assumption that changes in mortality rates by year due to changing risk factors are common across locations. Here we simultaneously adopt two approaches to relax that assumption, and hence strengthen the evidence for causality. We apply them to assess whether changes in PM_2.5 are associated with changes in mortality rates in a national cohort of Medicare participants in the U.S. In addition, as few previous cohort studies have controlled for temperature, we adjusted for mean warm season and mean cold season temperature.

2. Data and methods

2.1. Medicare cohort

We obtained the Medicare beneficiary denominator file, which contains information on all Medicare participants in the U.S., from the Centers for Medicare and Medicaid Services (RESDAC, 2018). We followed all beneficiaries’ ≥65 years in the contiguous U.S. from 2000 to 2016. Medicare insurance covers over 95% of the population ≥65 years of age in the United States. Medicare participants alive on January 1 of the year following their enrollment in Medicare entered the open cohort, and follow-up periods were calendar years. For the DID analysis, we computed an annual mortality rate in each ZIP code, in each group stratified by age (>84 or not), sex, race, and Medicaid coverage. This study was approved by the human subjects committee at the Harvard T. H. Chan School of Public Health.

2.2. Covariates

From the Medicare denominator file for each calendar year, we obtained the age, sex, race, ZIP code of residence for that year, eligibility for Medicaid for that year, and date of death (or censoring) of each participant. Age, ZIP code, and Medicaid eligibility were updated annually. This file is publicly available from the Centers for Medicare and Medicaid Services (RESDAC, 2018).

We obtained small area–level social, economic, and housing characteristic variables from the U.S. Census Bureau 2000 and 2010 Census Summary File 3 (Bureau, 2010) at the ZIP code tabulation–area level (ZCTA) and the American Household Survey for each year after 2010. These included percent of people ≥65 living in poverty, median household income, median house value, percent of owner occupied homes, percent black, percent Hispanic, population density, and education. We updated these variables for missing years by linearly extrapolating between the measured years. In addition, the county-level percentage of people who ever smoked and their mean body mass index (BMI) were obtained from the CDC Behavioral Risk Factor Surveillance survey (CDC, 2013), which were then assigned to each ZCTA within the county and updated each year. From the Dartmouth Health Atlas, we obtained percentage of Medicare participants who had a hemoglobin A1c test, a low-density lipoprotein cholesterol (LDLC) test, a mammogram, an eye exam, and a visit to an annual checkup for each year in each hospital catchment area and assigned it to all ZCTAs in that area (Wennberg and Cooper, 1996). We also computed the distance from each ZIP code centroid to the nearest hospital. To capture long-term smoking history of Medicare participants in each ZIP code, we computed their hospitalization rate for lung cancer by ZIP code for each year. This risks over-control because air pollution has been associated with increased risk of lung cancer. To capture year-to-year changes in mortality rates due to temperature, we downloaded daily temperature data on a 12 km grid from the NASA NLDAS-2 website (https://ldas.gsfc.nasa.gov/index.php/nldas/v2/models). We averaged all grid cells within the boundaries of a ZIP code, and constructed two measures for each year, the average temperature in the warm months (April–September) and in the cold months (October–March).

2.3. Exposure assessment

We estimated exposure using a validated prediction model calibrated to measurements at almost 2000 monitoring stations using an ensemble of machine learners that provided daily estimates for a 1 km grid of the contiguous U.S. (Di et al., 2019, 2020). In brief, the model used data from multiple sources including predictions of chemical transport models (GEOS-Chem, CMAQ, and MERRA-2), meteorological data, land-use terms, and satellite-based measures of aerosol optical depth, surface reflectance, and absorbing aerosol index. We trained a neural network, a random forest, and a gradient boosting machine to monitoring data from the United States Environmental Protection Agency (EPA) Air Quality System to generate daily predictions on a 1 × 1 km grid. The models were fit using data from all years. The three predictions for PM_2.5 were combined in a nonlinear geographically weighted regression. The model showed good performance with ten-fold cross validation on held out monitoring sites yielding an out of sample R² of 0.89 for annual average predictions of PM_2.5. Penalized splines showed linear relationships between observed and predicted PM_2.5 from 0 to 60 μg/m³. Predictions for all grid cells whose centroids were inside the ZIP code boundary were averaged for each year and assigned to participants in that ZIP code in that year.

2.4. Statistical analysis

The standard DID estimator for a continuous predictor posits that

$$E\left(Y_{ij}\right)={\beta }_0+{\beta }_{1}P{M}_{2.5}+{\beta }_2{C}_i+{\beta }_3{X}_t$$ (1)

where $Y_{ij}$ is the mortality rate in ZIP code $i$ in demographic group (by age >84 or not, sex, race, and Medicaid coverage) $j,C_i$ are the time-invariant or slowly changing confounders in ZIP code $i,X_t$ are the time varying confounders that are common across ZIP codes. The $C_i$ are controlled by fitting individual intercepts for each ZIP code. The time varying confounders are removed by fitting a nonlinear time trend; we used a natural spline function of year with 3 degrees of freedom, yielding:

$$E\left(Y_{ij}\right)={\beta }_0+{\beta }_{1}P{M}_{2.5}+{\delta }_i+ns(year,3)$$ (2)

where ${\delta }_i$ is a dummy variable for each ZIP Code. Since ZIP code is controlled, this model compares year-to-year variations around ZIP code average PM_2.5 and common time trend to year-to-year variations of mortality rates about ZIP code average and common time trend. Differences in e.g. SES, smoking, or diabetes between ZIP code are removed by the dummy variable for ZIP code. For a causal interpretation of the DID estimate to hold, we must assume that all the ZIP codes have parallel long-term time trends in mortality rates, other than those caused by different time trends in PM_2.5.

If covariates producing different time trends in mortality rate by ZIP code are not correlated with ZIP code specific PM_2.5 trends, the interpretation still holds. It would be preferable to further weaken this assumption.

We added two methods to relax the parallel trends assumption, and combined them in our analysis. We added to equation (2) terms for confounders that we have measured that change over time, possibly differentially by ZIP code. This will control for any temporal trends due to changes in these covariates, which include the SES, race, demographic, behavioral, and health access variables described above. Second, we grouped ZIP codes based on the above covariates and fit separate time trends in each group. We think that ZIP codes that are similar in racial composition, percent living below the poverty level, population density, smoking rates etc. Are more likely to have similar time trends in mortality rates than disparate ZIP codes. To accomplish this, we fit a principal component analysis to all the listed potential confounders and took the first 5 principal components. We classified each ZIP code into whether it was higher or lower than average on each of the 5 components, producing 32 categories of ZIP codes. In each of these 32 categories of ZIP codes, we fit separate splines for time trend and separate control for all of the covariates. This controls for time trends in measured covariates such as racial composition, median income, etc, and fits 32 separate time trends to the data to capture any trends unexplained by time trends in the measured covariates. It also allows the effects of the measured covariates to differ by the 32 different groups. In addition by performing analyses stratified by the 32 different groups we are also controlling by matching for the covariate clusters (e.g. SES and race) that characterize each group. Combining these, the final modeling approach is to fit 32 models (k = 1:32) and meta-analyze the 32 values of ${\mathrm{\beta }}_1$.

$$E\left(Y_{ij},k\right)={\beta }_0+{\beta }_{1k}PM25+{\delta }_i+{\delta }_{jk}+ns(year,3,k)+{\beta }_3{X}_{tk}$$ (3)

Here ${\delta }_i$ are indicator variables for each ZIP code, $X_{tk}$ are the time varying covariates whose time trends may differ by ZIP code and by which group ($\mathrm{k}$) the ZIP code is in, $ns(year,3,k)$ is a natural spline for time trend with 3 degrees of freedom for each group $k$, and ${\delta }_{jk}$ is an indicator variable for each age-race-sex-Medicaid stratum in group $k$. Results were combined over strata using a random effects meta-analysis.

Finally, equation (3) embodies an additive, rather than multiplicative model for the rate of mortality in each ZIP code-demographic group. This allows us to estimate the additive effect of PM_2.5 on the probability of dying, provides more interpretative interaction terms, and provides a marginal effect estimate (i.e. not dependent on the distribution of the covariates, as a multiplicative model would be). Additive probability or rate models give unbiased estimates of effect just as the more usual logistic models, but biased estimates of standard errors (Caudill and Jackson, 1989). Therefore have used robust standard errors to estimate the confidence intervals. In a second analysis, we reran the analysis on data restricted to persons whose exposure was always below 12 μg/m³, the U.S. standard for PM_2.5.

3. Results

Table 1 shows the characteristics of the Medicare cohort between 2000 and 2016. There were 623, 036, 820 person-years of follow-up during the study, and 29, 481, 444 deaths. 85.4% of the participants were white, and 12.9% were covered by Medicaid, which provides additional benefits to the poor. The mean PM_2.5 during the study was 10.3 μg/m³.

Table 1.

Shows the distribution of covariates and exposure in the Medicare Cohort

Variable	Values
Year
Mean (SD)	2009.5 (4.90)
Median [25%, 75%]	2010 [2004, 2013]
Male	42.8%
Race
Black	8.4%
Other	6.2%
White	85.4%
Age > 84	13.2%
Medicaid Coverage	12.9%
ZIP Code Covariates
Median Income
Mean (SD)	$53,177 ($22,082)
Median [25%, 75%]	$47,998 [$38,030, $63,031]
Median House Value
Mean (SD)	$200,139 ($159,728)
Median [25%, 75%]	$150,400 [$98,600, $240,300]
Percent ZIP code Black
Mean (SD)	11% (17.9%)
Median [25%, 75%]	3.7% [1.1%, 12.0%]
Percent ZIP code Hispanic
Mean (SD)	12.6% (16.4%)
Median [25%, 75%]	5.3% [2.1%, 14.6%]
Percent >65 below poverty
Mean (SD)	9.5% (6.5%)
Median [25%, 75%]	7.9% [5.3%, 11.8%]
Percent Low Education
Mean (SD)	25.3% (14.7%)
Median [25%, 75%]	22.6% [14.2%, 33.7%]
Percent with annual Mammogram
Mean (SD)	63.7% (7.2%)
Median [25%, 75%]	63.9% [59.2%, 68.2%]
Percent with ambulatory Visit
Mean (SD)	77.8% (6.2%)
Median [25%, 75%]	79.0% [74.4%, 82.1%]
Population Density (persons/mi2)
Mean (SD)	3397 (9032)
Median [25%, 75%]	967 [167, 3353]
Percent Owner Occupied
Mean (SD)	68% (16%)
Median [25%, 75%]	70.8% [59.8%, 79.2%]
Mean BMI (kg/m2)
Mean (SD)	27.5 (1.58)
Median [25%, 75%]	27.3 [26.7, 28.0]
Distance to nearest hospital (km)
Mean (SD)	6.5 (7.4)
Median [25%, 75%]	3.90 [1.98, 8.07]
Ever Smoker
Mean (SD)	46.2% (6.8%)
Median [25%, 75%]	46.2% [41.8%, 50.4%]
Percent annual HbA1c test
Mean (SD)	83.1% (4.9%)
Median [25%, 75%]	83.7% [80.5%, 86.3%]
Lung Cancer Rate (× 10−4)
Mean (SD)	3.9 (2.8)
Median [25%, 75%]	3.3 [1.9, 4.9]
Percent annual LDL
Mean (SD)	79.5% (6.2%)
Median [25%, 75%]	80.1% [76.1%, 83.5%]
Percent Annual Eye Exam
Mean (SD)	67.4% (6.4%)
Median [25%, 75%]	67.1% [63.9%, 71.0%]
PM2.5 (μg/m3)
Mean (SD)	10.3 (3.1)
Median [25%, 75%]	9.8 [7.9, 12.0]

In the meta-analysis of the results of the 32 strata-specific DID analyses, we found that the probability of dying in each year increased by 3.85 × 10⁻⁴ (95% CI 1.95 × 10⁻⁴, 5.76 × 10⁻⁴) for each 1 μg/m³ increment in PM_2.5 in that year. The I² statistic for heterogeneity was 42%. When we restricted our analysis to persons whose exposure was always below 12 μg/m³ during the follow-up period, we found a larger effect size, with the probability of dying in each year increased by 4.26 × 10⁻⁴ (95% CI 1.43 × 10⁻⁴, 7.09 × 10⁻⁴) per 1 μg/m³ increase in PM_2.5. Interaction terms for male gender, age >84, and race were fit in the full data. Sex was a significant modifier (p for interaction <0.001), with larger effects in males (6.81 × 10−⁴, 95% CI 4.14 × 10⁻⁴, 9.48 × 10⁻⁴) then females (1.20 × 10⁻⁴, 95% CI −8.80 × 10⁻⁵, 3.29 × 10⁻⁴). These results are shown in Fig. 1. There was no interaction by age. Interaction models for race did not converge because residential segregation in the U.S. resulted in groups with too few Blacks or Asians and other races. Instead, we reran the analysis without separate models for each of the 32 groups. There was no significant interaction by race.

Fig. 1.

Shows the effect size estimate (absolute increase in the death rate for each 1 μg/m³ increase in PM_2.5 exposure, and 95% Confidence Interval) for the entire Medicare Cohort in 2000–2016 (All), for only persons never exposed to PM_2.5 concentrations above 12 μg/m³ (low) during the follow-up period, for males in the entire Medicare Cohort (males) and for females in the entire Medicare Cohort.

4. Discussion

Using a difference in differences design applied to a linear rate model, we found that each 1 μg/m³ increment in PM_2.5 was associated with a 3.85 × 10⁻⁴ increase in the probability of dying in a given year. If the difference in differences assumptions are met, this is a causal increase. We believe they are met for the following reasons. First, since this design controls for each ZIP code, all individual and neighborhood level confounders that change little over time are controlled, whether measured or not. This includes most of the variables (e.g. SES, smoking history, diet) that have be posited as potential confounders. Consequently, only time varying factors can be confounders. Second, we controlled for potential confounding in each ZIP code due to time trends in median household income, median home value, percent owner occupied housing, percent of ZIP code that is Black, percent of households that are Hispanic, percent of persons aged 65 or older living in poverty, smoking rate, BMI, Medicaid eligibility, educational attainment, population density, lung cancer rates, multiple measures of the adequacy of medical care, and summer and winter temperature. Third, we grouped the ZIP codes by these factors, and fit separate nonlinear time trends within each of 32 groups to capture any remaining time trends due to omitted confounders could differ between groups, but would be similar within group. This approach effectively looks at the within ZIP code fluctuations in exposure around the ZIP code mean, trend due to measured time-varying covariates, and common trends by group of ZIP codes. It compares that to the same deviation in mortality. Such an approach, looking at yearly deviations from trend and ZIP code mean in exposure and outcome, is inherently examining the relationship of changes in exposure to changes in outcome. This also addresses the issue of whether previous studies effects are due to primarily recent exposure, or reflect long term exposure, including when pollution concentrations were higher. The dummy variable for each ZIP code controls for long term exposure at that ZIP code, and the removal of nonlinear time trends during the period under study focuses the exposure variable on the year of the death. EPA Regulatory Impact Analyses spread the estimated mortality effects out over a 20 year period. This study provides an estimate of immediate impact. Because our study incorporates 17 years of follow-up, each year has a new exposure, and a new effect.

In addition this paper adds to the sparse literature controlling for temperature in studies of long-term exposure to air pollution, which some have argued is an important confounder. Further, we estimated the probability of dying in a year, which is more easily interpretable than an instantaneous hazard rate, and by using an additive rather than multiplicative model we estimated the marginal effect if PM_2.5, not the conditional effect estimated by Cox’s proportionate hazard model. This allows one to estimate attributable deaths in health impact assessments without making further, possibly implausible assumptions required when using a conditional estimate.

Some scientists, including the current chair of EPA’s Clean Air Scientific Advisory Committee (CASAC), assert that studies using standard epidemiological methods should be given little weight in revising the NAAQS, and propose restricting to studies using causal methods, and particularly ones showing changes in air quality are associated with changes in mortality (CASAC, 2019). The recent meetings of EPA’s CASAC highlighted the importance of these issues (CASAC, 2019). Their main criticism is that traditional approaches only show associations that may be confounded, vary depending on modeling approaches, and do not inform causality, which can only be addressed by causal methods. They also emphasize that unmeasured variables, particularly individual characteristics, socioeconomic status, and temperature may confound the published literature (Cox and Popken, 2015). EPA recently proposed not tightening the NAAQS for PM_2.5, relying on these arguments. This paper provides an analysis using a causal method, controlling for temperature and socioeconomic status, and all individual and area level potential confounders, measured or unmeasured, that vary slowly over time.

That EPA proposal also asserted there was insufficient evidence of a causal association at lower levels. When we restricted our analysis to include only persons who never experienced concentrations above 12 μg/m³ during 17 years of follow-up we found a somewhat larger effect estimate of 4.26 × 10⁻⁴ (95% CI 1.43 × 10⁻⁴, 7.09 × 10⁻⁴) per 1 μg/m³ increase in PM_2.5.₅. This indicates that the current U.S. and E.U. standards are not sufficient to protect public health, and that the WHO standard of 10 μg/m³ is unlikely to protect public health.

Other studies have applied causal modeling methods to air pollution, primarily propensity score methods (Abu Awad et al., 2019; Schwartz et al., 2018; Wang et al., 2017; Wei et al., 2020; Wu, 2020; Yitshak-Sade, 2019). These methods use the relationship between exposure and confounders to render the exposure independent of all of the measured confounders, and hence mimic a randomized trial. They have all reported that PM_2.5 increases mortality rates. The difference in differences approach complements those studies by its ability to deal with unmeasured confounders. All personal and small area time invariant or slowly varying confounders are removed by design, whether measured or not. All confounders whose time trends are due to measured time-varying confounders or similar within groups defined by race, SES, medical access, and behavioral characteristics are controlled whether measured or not. Hence, this paper adds assurance about many possible unmeasured confounders to the large literature of associational studies and smaller literature of propensity score-based models that provide causal estimates. Together, they provide strong evidence for a causal effect of PM_2.5 on mortality rates.

Since we estimate the probability of dying in each year and not a hazard rate, our effect sizes are not directly comparable to the other causal modeling studies. Compared to the larger literature, a recent meta-analysis of then extant cohort studies estimated the effect size at 10 μg/m³ (the mean concentration in this study) as a 1.29% increase in the rate per μg/m³ increase in PM2.5, (95% CI 1.09%, 1.50%) (Vodonos, 2018). The annual mortality rate in the Medicare cohort was 4.7 × 10⁻². A 1.29% increase in that rate is an additive increase of 6.1 × 10⁻⁴. The results from a previous Cox regression analysis of the Medicare cohort from 2000 to 2012 translate to an additive increase of 3.4 × 10⁻⁴. These are similar to our results. Hence these other studies are unlikely to have been confounded by temperature, or slowly varying SES, racial, and behavioral factors which this study controlled for.

Nor are these effects small. Multiplying our effect estimates by the total person-years in the Medicare cohort, we estimate that had everyone had 1 μg/m³ lower exposure, 239,900 early deaths would have been avoided during the follow-up period. EPA’s National Contingency Plan (40 C.F.R. § 300.430(d) (1)) states that the range of acceptable lifetime risks (of developing cancer) for carcinogens should be set between 1 in 10,000 and 1 in a million over a 70-year lifetime. Thus, when EPA considers regulations for carcinogens, it typically regulates if lifetime risks exceed 1 in a hundred thousand. In contrast, 1 μg/m³ of exposure below the current EPA standard for only 1 year results in an increased risk of dying of 4.26 per ten thousand in our study.

Our finding has limitations. First, DID analyses depend on the change over time in other ZIP codes with different changes in PM_2.5 to serve as controls for changes over time in outcome that may have occurred independent of exposure. If the time trends in the ZIP codes are different, this control will fail. We have dealt with this by controlling for time trends in measured covariates and grouping ZIP codes into 32 groups that are similar on age, sex, race/ethnicity, SES, and access to medical care, and doing the analysis separately within each group, arguing that the time trends in mortality rates will be similar within group. However, we cannot exclude the possibility that they are not. Second, our exposure estimates are not perfect. While an out of sample R² of 0.89 is high, there is still some exposure error, which may bias estimates. In addition, personal exposure within a neighborhood varies around the neighborhood ambient concentration. However, we believe most of that difference is likely to be Berksonian error, and hence not bias coefficients. Moreover, the principle reason for the differences between ambient and personal exposure are behavioral (more driving, more cooking, etc), and incorporating exposure related to those factors would require controlling for other related risk factors (e.g. stress from driving) that are not confounders of the neighborhood ambient concentrations. Hence, this exposure error is beneficial from the point of view of reducing confounding, as has been pointed out previously (Weisskopf and Webster, 2017).

In conclusion, we have found an effect of PM_2.5 on daily deaths using a causal modeling approach robust to unmeasured confounders. The effect size is similar to those reported in associational studies, suggesting that unmeasured confounders are not an issue with them, and is large enough to indicate that reducing PM_2.5 concentrations in the U.S. could save tens of thousands of premature deaths each year.